Time of Day
When it comes to Time of Day, there are basically two flavors in most games:
1) Time is locked on a per-level basis.
2) Time is constantly advancing, with a sun (and moon) that move across the sky.
It should probably go without saying that a game where the sun is always moving means a lighting system that is dynamic in nature, with real-time shadows being cast.
If the sun is constantly moving across the sky, that means the shadows are moving as well, and that means no baked lighting. There are some hybrid systems, where the building interiors are lightmapped, and the outside world is fully dynamic, but there are limitations with this as well.
The problem is that if you have an open-world game where the sun is always moving, it becomes much more difficult to set up "hero moments" or maybe I should say "visual hero moments", because you have no idea what time of day the player may come across a given situation in the game. You're basically saying "Well, I hope it looks good when this really important thing happens, because it might be noon, or it might be midnight."
My personal preference is to have time of day locked per level. You still get the feeling as you play through the game that time is passing (since there are varying time of day and weather changes between levels), but knowing exactly where the sun is gives you much more of an opportunity to stage dramatic moments and vistas.
Games that have a lot of interiors can be especially difficult to light in a dynamic system, but lend themselves to great possibilities if lightmapping is being used.
Which brings us to the Lightmaps vs. Real-time situation.